Information on Result #547995
There is no linear OA(8112, 270, F8, 95) (dual of [270, 158, 96]-code), because construction Y1 would yield
- OA(8111, 134, S8, 95), but
- the linear programming bound shows that M ≥ 3213 718744 248367 464211 966828 793200 685277 723323 269317 408810 044111 174024 201867 677763 903619 161246 026196 671187 301423 896682 561536 / 165729 471662 280587 916075 > 8111 [i]
- linear OA(8158, 270, F8, 136) (dual of [270, 112, 137]-code), but
- discarding factors / shortening the dual code would yield linear OA(8158, 266, F8, 136) (dual of [266, 108, 137]-code), but
- residual code [i] would yield OA(822, 129, S8, 17), but
- 1 times truncation [i] would yield OA(821, 128, S8, 16), but
- the linear programming bound shows that M ≥ 1 008968 613742 170487 095115 575000 563712 / 108734 057573 457133 > 821 [i]
- 1 times truncation [i] would yield OA(821, 128, S8, 16), but
- residual code [i] would yield OA(822, 129, S8, 17), but
- discarding factors / shortening the dual code would yield linear OA(8158, 266, F8, 136) (dual of [266, 108, 137]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OOA(8112, 270, F8, 2, 95) (dual of [(270, 2), 428, 96]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(8112, 270, F8, 3, 95) (dual of [(270, 3), 698, 96]-NRT-code) | [i] | ||
| 3 | No digital (17, 112, 270)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |